Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #24906060 | C2 | semidirect |
| 3. #24905897 | C2 | semidirect |
| 4. #24905816 | C2 | semidirect |
| 5. #24905373 | C2 | semidirect |
| 6. #24905353 | C2 | semidirect |
| 7. C83×#2971 | C2 | semidirect |
| 209. #2971 | D83 | semidirect |
| 215. C83 | #9350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916957 | 2 |
| #24906060 | 2 |
| #24905897 | 2 |
| #24905816 | 2 |
| #24905373 | 2 |
| #24905353 | 2 |
| C83×#2971 | 2 |
| #9350 | 83 |